I would say you may be able to use portions of a cities infrastructure, but only on such a small scale that the 'cons' of trying to re-inhabit a large city would out way the 'pros'. And the larger the city, the more complex all the utility infrastructure would be.
Electricity. Accepting post-apocalyptic conditions of no grid, then a building in a city has no advantage over a building anywhere else. You will have to supply power one building, perhaps even one circuit at a time. Many commercial buildings, and utility systems such as pumps, in a city will require different voltages and phases then a survivor group can generate. Best bet here might be some locations with their own generators, but again that's a finite resource. No more fuel, no more spare parts.
Water. Most cities get their water from two sources:Intake and treatment from rivers, and pumped from underground wells. Both of these require electricity, and on a scale generally not available to 'survivors'. So the CITIES infrastructure again provides nothing above that of an individual building anywhere else. The best water source is a flowing river, in or out of a city, but in the city how contaminated is it?
Sewers. Once again, the larger the city, the higher the probability that it requires electricity running on a large scale. Pumping stations are required in
most city locations. It would be amazing to be able to run sewer lines through an entire city 'on grade'. Secondly, your toilet wont flush without the water system connected to it, or you dump a bucket of water into it after use.
Sewers are one location where rural situations would have an advantage, as they usually are self contained, and do 'just flow downhill'.Even those, however, eventually fill up.
Food. Without knowledge of the nature of the apocalypse, its hard to say what availability of food resources might be. In most events such as approaching hurricanes or such, you notice many stores with empty shelves, so stores and restaurants are a finite resource at best, or more likely have been emptied completely during the initial 'event'.
Farming.If you have to grow your own food, it takes acres of open land to raise enough food to support any sizable population. The city has acres of buildings. Those with parks, many rely on sprinklers to keep them green, so...
Manufactured Resources. This is the one aspect that the city may have an advantage over a more rural setting would be the vast amount (if not destroyed by whatever event) of manufactured materials. Mining the city for aluminum, glass, containers, ect, would possibly be of value in the long run. The vast variety of things to be found would be overwhelming. But directly affecting survival that you can't find elsewhere?
Problems. Whether war or plague, the cities will be the largest targets. Depending on 'the event', the cities will suffer fires, looting, and death on a scale most have not seen. No one will be there to clean this up, so if all but a handful have died, then there are thousands or millions of dead in the streets and homes, lots of disease, lots of decay infecting everything around.
The other issue being other groups of survivors will be attracted to the city, and they might not be friendly to your group...
All said, it seems any infrastructure being used will have to be provided at the individual building level, so the city would have no advantage over any other location. A smaller location then a large city provides the same shelter, wiring and pipes, but at a scale which might be overcome to restore some semblance of Society again.